Weaver, 28, would be a free agent following the 2012 season. The Angels and Weaver's agent, Scott Boras, were more than $1 million apart when they swapped arbitration figures about a one-year deal earlier this month. Weaver is asking for $8.8 million while the Angels have offered $7.45 million. Weaver made $4.63 million last year.
General manager Tony Reagins said it's too early to predict whether the sides could reach a long-term deal before an arbitration hearing, scheduled for late February.
"I have no idea," Reagins said. "Any time you have dialogue, it's positive. We'll see."
Weaver led the majors with 233 strikeouts last season. He is 64-39 with a 3.55 ERA in five major league seasons, all with the Angels. Many people have speculated that Weaver could follow his mentor, John Lackey, out of town when the time comes because of Moreno's poor relationship with Boras.
Slugger Kendry Morales, who has three more seasons left before free agency, also is a Boras client.
Moreno said he still won't speak directly with baseball's most powerful agent, but that Reagins and other Angels employees are free to conduct business with him. The bad blood stems from messy negotiations to keep Mark Teixeira in Anaheim in 2008.
"My mother always told me, 'If you don't have something nice to say about somebody, don't say anything,'" said Moreno, speaking at Wednesday's introduction of newly acquired outfielder Vernon Wells. "I don't have to deal with anybody I don't have to deal with. That's the way I live my life."
Mark Saxon covers the Angels for ESPNLosAngeles.com.